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Plurisubharmonic functions in almost complex manifolds. (Fonctions PSH sur une variété presque complexe.) (French. Abridged English version) Zbl 1013.32019
Summary: Let $$(M,J)$$ be an almost complex manifold. An upper semi-continuous map $$u:(M,J)\to [-\infty,+ \infty[$$ is said to be plurisubharmonic if $$u\circ \varphi$$ is subharmonic for every pseudo-holomorphic curve: $$\varphi: (\Delta, J_0)\to (M,J)$$. By using regularization techniques for currents and Taylor series expansions in suitable coordinates with respect to the structure $$J$$, we prove that an upper semi-continuous map $$u:(M,J)\to [-\infty,+ \infty [$$ which is not identically equal to $$-\infty$$ is plurisubharmonic if and only if the $$(1,1)$$-part of $$-dJ^*du$$ is (semi-)positive as a current.

##### MSC:
 32U05 Plurisubharmonic functions and generalizations 32Q60 Almost complex manifolds
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##### References:
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